Abstract
In the current paper, we study the structure of Jordan ideals of a 3-prime near-ring which satisfies some algebraic identities involving left generalized derivations and right centralizers. The limitations imposed in the hypothesis were justified by examples.
Highlights
A right near-ring is a nonempty set N equipped with two binary operations +Iraqi Journal of Science, 2021, Vol 62, No 6, pp: 1961-1967N, an additive mapping F : N → N is said to be a left generalized derivation associated with d if F(xy)= d(x)y + xF(y) for all x, y N
The commutative property of 3-prime near-rings with some suitable constraints on derivations and generalized derivations was established by various authors
Our aim in the current paper is to extend these results of Jordan ideals on 3-prime near-rings admitting a nonzero left generalized derivation
Summary
A right near-ring (resp. left near-ring) is a nonempty set N equipped with two binary operations +. Et al (2014) [3] initiated the study of the concept of Jordan ideals on near-rings; ‘An additive subgroup J of N is said to be Jordan left Boua et al studied commutativity of 3-prime nearrings admitting suitably constrained additive mappings, as derivations, generalized derivations and left multipliers, satisfying certain differential identities on Jordan ideals of 3-prime near-rings. It is natural to continue this line of investigation for comparable results for 3-prime near-rings having other additive mappings with Jordan ideals. We shall attempt to generalize the known result and study the commutativity of Jordan ideal in 3-prime near-rings satisfying certain functional identities involving left generalized derivations and right centralizers
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